Many models exist to simulate pollutants emitted by materials in test chambers for a short period of time or to simulate the evolution pollutants in large rooms. No model exists to simulate steady state concentration of vapors in enclosure close to adsorption equilibrium conditions. A model is on the stage of development to simulate evolution of pollutants in enclosure in preservation contexts in extended periods. The goal is to be able to simulate different situations such as leakage performance of display cases, efficiency of sorbents and harmfulness of emissive materials in enclosures.
The model is based into two combined principles: diffusion based on the first Fick law and adsorption isotherm. The first Fick law is based on the hypothesis that rate of mass transfer through unit area of a material section is proportional to the concentration gradient to the section. The adsorption isotherm expresses the equilibrium condition between a material and the vapor. Different empirical equations exist to express the equilibrium. Key equations used for the model are:
|Using Linear:||dMM/dt = s(-aCM + bCE)|
|Using Langmiur:||dMM/dt = s(-aCM + b(gCE/(1 + gCE)))|
|Using Freundlich:||dMM/dt = s(-aCM + bCEg)|
|MM:||mass of the compound in the material|
|CM:||concentration of the compound in the material|
|CE:||concentration of the compound in the enclosure|
|s:||surface of the material|
|a, b, g:||constants|
Since the model is based on first Fick law and adsorption isotherm, some assumptions have been made:
- negligible fluctuations of temperature and atmospheric pressure.
- the volume of the enclosure is not bigger than two cubic meters.
- uniform concentration of the compound in the material and in the enclosure.
- fast diffusion in the material: the material should be either a thin film or be very porous.
- hysteresis associated with sorption and desorption cycles are negligible.
A database contains a list of the best fit model for specific pollutant - material systems. Up to now, the model can simulate many scenarios: the evolution of pollutant can be done with the presence of up to three materials inside the enclosure. Information such weigh and surface of the materials must be provided as well as the initial pollutant concentration in materials. Generation or disappearance of pollutants can be done to simulate new pollutant formed during degradation processes or disappearance of pollutants associated to irreversible reactions. Leakage rates of the enclosure are variable and the outside concentration can be linear, cyclic or having a shape peak at a specific time. The duration of the simulation is variable from few hours to few years. Runge- kutta method is used to solve the differential equations and the model is written in C++ codes.
As future step, more experimental data on pollutant - material interactions must be obtained. There is also interest to improve the model by considering the second Fick law which deal with the diffusion into materials.
Jean Tétreault*, Conservation Scientist
Canadian Conservation Institute, 1030 Innes Road Ottawa, Ont. K1A 0M5, Canada
Computing Devices Canada, 3785, Richmond, Nepean, Canada
Patrick Olivier, Senior Software Development Engineer
Imaging Dianostic Systems, Inc., 6531 NW, 18th Court, Plantation, FL 33313, USA.
(*) Author to whom correspondence may be addressed
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